3D Distribution of Molecular Gas in the Barred Milky Way
Martin Pohl
arXiv:0712.4264v1 [astro-ph] 27 Dec 2007
Department of Physics and Astronomy, Iowa State University
Ames, Iowa 50011-3160, USA
Peter Englmaier
Institut für Theoretische Physik, Universität Zürich, 8057 Zürich, Switzerland
Nicolai Bissantz
Fakultät für Mathematik, Ruhr-Universität Bochum, 44780 Bochum, Germany
[email protected]
ABSTRACT
We present a new model of the three-dimensional distribution of molecular
gas in the Milky Way Galaxy, based on CO line data.
Our analysis is based on a gas-flow simulation of the inner Galaxy using
smoothed-particle hydrodynamics (SPH) using a realistic barred gravitional potential derived from the observed COBE/DIRBE near-IR light distribution. The
gas model prescribes the gas orbits much better than a simple circular rotation model and is highly constrained by observations, but it cannot predict local
details. In this study, we provide a 3D map of the observed molecular gas distribution using the velocity field from the SPH model. A comparison with studies
of the Galactic Center region suggests that the main structures are reproduced
but somewhat stretched along the line-of-sight, probably on account of limited
resolution of the underlying SPH simulation. The gas model will be publicly
available and may prove useful in a number of applications, among them the
analysis of diffuse gamma-ray emission as measured with GLAST.
Subject headings: ISM: structure, Galaxy: kinematics and dynamics
1.
Why another deconvolution of gas data?
Models of the distribution of interstellar gas reflect the structure of the Milky Way
Galaxy and have therefore considerable merit in themselves. In addition, they are also
–2–
highly valuable for a variety of other applications, among them the physical analysis of diffuse Galactic gamma-ray emission (Bertsch et al. 1993; Hunter et al. 1997; Pohl & Esposito
1998). Knowledge of the gas distribution is essential for studies of the large-scale cosmic-ray
distribution in the Galaxy, as well as for investigations of small-scale variations in the density and spectrum of cosmic rays. The upcoming launch of GLAST, a GeV-band gamma-ray
observatory of unprecedented sensitivity, makes it desirable to have an up-to-date model
of the three-dimensional distribution of the ISM. There are two main reasons why a new
study would be required: The various components of interstellar gas are traced by their
line emission, and the quality of the line data available today is much higher than it was in
the Nineties. Also, it is now well established that the Galaxy contains a central bar (e.g.
Babusiaux & Gilmore 2005; Benjamin et al. 2005), which causes non-circular motion of interstellar gas in the inner Galaxy, thus changing the kinematic relation between the location
on the line-of-sight and the velocity relative to the local standard of rest (LSR).
Here we report results for the deconvolution of CO1→0 data for the entire Galactic plane
(Dame et al. 2001). For that purpose we use a gas-flow model derived from smoothed particle
hydrodynamics (SPH) simulations in gravitational potentials based on the NIR luminosity
distribution of the bulge and disk (Bissantz et al. 2003). Besides providing a more accurate
picture of cloud orbits in the inner Galaxy, a fundamental advantage of this model is that it
provides kinematic resolution toward the Galactic Center, in contrast to standard deconvolution techniques based on purely circular rotation (Nakanishi & Sofue 2006). Sawada et al.
(2004) used OH-absorption data in comparison with CO emission lines to infer the distribution of molecular gas in the inner few hundred parsecs, and found it strongly influenced by
the bar. Our model should incorporate the imprint of the bar over the entire inner Galaxy.
Therefore, our result does not suffer from a strong finger-of-god effect like in the classical
paper by Oort et al. (1958).
Because any deconvolution will introduce artefacts, we test our procedure on simulated
line spectra, which allows us to identify artefacts that are present in the final gas model. We
investigate three different gas-flow models for the inner Galaxy, one of which is intentionally
distorted so it no longer corresponds to a SPH simulation that has been adapted to gas data.
In the Galactic-Center region, for which studies with alternative methods like OH absorption have been performed, we find the gas distribution in our model generally consistent
with those earlier results, provided one accounts for the existence of barred gravitational potential. On account of limited resolution both in the gas flow model and the deconvolution
the central molecular zone appears somewhat stretched along the line-of-sight, though.
–3–
2.
2.1.
The method
The CO data
The CO1→0 emission line is the best available tracer of molecular gas, even though the
exact relation between the integrated line intensity and the column density of molecular
gas, usually referred to as the X-factor, is known to vary with Galactocentric radius and
metallicity (Sodroski et al. 1995; Arimoto et al. 1996; Oka et al. 1998; Strong et al. 2004;
Nakagawa et al. 2007). The X-factor can be determined at specific locations through the line
signal of CO with rare isotopes of either carbon or oxygen using various assumptions for the
radiation transport (Dickman 1978; Dahmen et al. 1998; Wall 2006) or through absorption
measurements of H2 and CO in the UV (Burgh et al. 2007).
We use the composite survey of Dame et al. (2001), which comprises more than 30
individual surveys of CO1→0 emission that together cover the entire Galactic Plane. The
data were taken with the CfA 1.2-m telescope and a similar instrument in Chile. The
angular resolution is about 1/6 of a degree, and the sampling is slightly better than that
with 1/8 of a degree. The velocity sampling is 1.3 km/s and the rms noise is around 0.3 K
per channel, but varies slightly over the Galactic Plane. The advantage of this survey lies in
its sensitivity, the sampling, and the uniformity.
CO surveys have been conducted with significantly higher angular resolution, for example the FCRAO Outer Galaxy Survey (Heyer et al. 1998), the Massachusetts-Stony Brook
Galactic Plane CO Survey (Clemens et al. 1986), or the NANTEN Galactic Plane Survey.
These surveys either cover only a small part of the sky or are significantly undersampled,
thus somewhat compromising their applicability in studies of the large-scale distribution of
molecular gas in the Galaxy. Also, considering the width of the point-spread function and
the photon statistics at high energies, the effective angular resolution of GLAST is not better than that of the CfA survey, and thus CO data of higher angular resolution may not be
needed. We have therefore decided to solely use the CfA survey with a sampling of 1/8 of a
degree. By applying the appropriate smoothing we have verified, that the publicly available
high-resolution surveys are perfectly consistent with the lower-resolution CfA survey, so by
using the CfA survey we have not lost any significant information other than the detailed
distribution on scales below 1/6 of a degree.
–4–
2.2.
The Galactic bar
While bars were clearly observed in other galaxies, absorption of visible light by dust
has for a long time impeded searches for similar structures in our Galaxy. The availability
of sensitive infrared detectors in recent decades has finally permitted increasingly accurate
studies of the structure of inner Galaxy. Today, the observational evidence for the existence
of a Galactic bar is very strong (Gerhard 2001), but some uncertainty remains concerning
the characteristics of that bar. As an example, using Spitzer data Benjamin et al. (2005) find
a bar with half-length of Rbar ≃ 4 kpc (for a GC distance of 8 kpc) at an angle of φ ≃ 45◦ ,
whereas the NIR photometry data of Babusiaux & Gilmore (2005) suggest Rbar ≃ 2.5 kpc
and φ ≃ 22◦ . Using COBE/DIRBE L-band data and giant-star counts Bissantz & Gerhard
(2002) determine the bar to be oriented at an angle φ ≃ 23◦ with spiral arms emerging at
R = 3.5 kpc.
Based on their earlier analysis of the COBE L-band data (Bissantz et al. 1997), Englmaier & Gerhard
(1999) have calculated the resulting gravitational potential and modelled the gas flow for the
Milky Way inside the solar circle using smoothed particles hydrodynamics in those potentials.
It is worth noting, that this model is non-parametric and has virtually no free parameters,
except the bar orientation is not tightly constrained by the observations of NIR-light, the
microlensing event rate, the red clump giant distribution, and the CO kinematics. Later, in
a refined analysis, also the spiral arm pattern was taken into account (Bissantz et al. 2003).
To select the best fitting models of the gas flow, Bissantz et al. (2003) compared simulated
longitude-velocity diagrams with the main features of observed CO emission for a certain
range in Galactic longitude.
Here we use the velocity field from their gas flow models instead of a simple circular
rotation curve to determine a distance-velocity relation that will allow us to find the location
of molecular gas as traced by CO1→0 line emission. It is important to note that the noncircular flows imposed by the bar provide kinematic resolution even toward the Galactic
Center on account of the radial motion of gas. We use three different velocity-field models
in this work. The first is the standard model of Bissantz et al. (2003), which is based on a
bar inclination angle φ = 20◦ . As alternative we test a model with φ = 30◦ that, according
to Bissantz et al. (2003), can also reproduce the main features in position-velocity diagrams
of CO line data. The third model is the standard model rotated by 20◦ , so the bar would
make an angle of φ = 40◦ to the line-of-sight and line-of-sight velocities are no longer in
accord with the observed velocities of gas. The purpose of that third model is to show the
effect of an ill-fitting gas-flow model, and the deduced gas distribution in the Galaxy should
be seriously distorted in this case.
Fig. 1 shows the line-of-sight velocity for the standard flow model as a function of
–5–
distance toward the Galactic Center. For comparison, Fig. 2 gives the CO line spectrum
for the same line-of-sight. For the bulk of the line signal at velocities around 50 km/s we
now find two possible distance solutions, one near 8 kpc and the other one close to 10 kpc.
To be noted from Fig. 1 is also that for many velocities we find a multitude of possible
distances, e.g. eight different solutions near zero velocity for the line-of-sight toward the
Galactic Center, not just two as in the case of purely circular rotation. Also, the gas flow
model does not fully cover the observed range of velocities, as the spectrum in Fig. 2 shows
a line signal of about 1 K at -150 km/s and of 2 K at 160 km/s, which is far beyond the
range of velocities for which distance solutions exist.
2.3.
Deconvolution technique
Many quantities are practically expressed in galactocentric cylinder coordinates (r, φ, z),
but transformations are easier to follow in galactocentric Cartesian coordinates ~r. In those
coordinates any location is described by a vector ~r = (r cos φ, r sin φ, z), and the sun is
located at ~rs = (R0 , 0, z0), where (e.g. Joshi 2007)
R0 = 8 kpc
z0 = 15 pc
(1)
Let us write the distance vector ~y = ~r − ~rs in the form
~y = (−D cos l cos b, −D sin l cos b, D sin b) = (−P cos l, −P sin l, Q)
(2)
where we used heliocentric Galactic coordinates, D is the true distance, and P is the distance
as projected on the Galactic plane. For a given CO line spectrum we know the direction
in Galactic coordinates l,b and can relate r to the line-of-sight velocity. The solution for P
then is
q
P = R0 cos l + r 2 − R02 sin2 l
r ≥ R0
(3)
q
r ≤ R0
(4)
P = R0 cos l ± r 2 − R02 sin2 l
where always
r ≥ R0 | sin l|
(5)
and also
D cos b = P
z = z0 + P tan b
(6)
Throughout this paper we assume that the gas flow in the Galaxy is independent of z, so
the flow pattern known for the mid-plane also applies at any height above the plane. This
approximation should not cause much error because molecular gas is usually found close to
–6–
Fig. 1.— The line-of-sight velocity of interstellar gas as a function of distance for the Galactic
Center direction, based on the standard gas flow model of Bissantz et al. (2003). The model
successfully predicts large radial velocities, but offers a large variety of possible distance
solutions near zero velocity.
–7–
Fig. 2.— The CO1→0 line spectrum for the Galactic Center direction as given by the CfA
data cube. For most of the line signal distances can be found, but some intensity at forbidden
velocities remains.
–8–
the mid-plane. This assumption holds when |z| << r, i.e. it breaks down very close to the
Galactic Center.
If we had a purely circular gas flow with rotation curve V (r), then the uncorrected
radial velocity would be
R0
V (r) − V (R0 ) sin l cos b
(7)
VLSR (l, b, P ) =
r
where Eq. 4 is used to link the projected distance P to the Galactocentric radius r. The
proper motion of the sun relative to the local standard of rest has a line-of-sight component
of (Dehnen & Binney 1998)
VLSR,⊙ = (10. cos l cos b + 5.2 sin l cos b + 7.2 sin b) km s−1
(8)
which we can account for by subtracting it from the radial velocity. The corrected, effective
velocity then is
Veff (l, b, P ) = VLSR (l, b) − VLSR,⊙
(9)
We use Eqs. 7 and 9 to estimate the gas velocity for all Galactocentric radii larger than
R0 , i.e. outside the solar circle, where the gas orbits are assumed circular with constant
velocity V = V0 = 210 km/s. The actual rotation velocity of gas in the outer Galaxy
depends somewhat on the choice of R0 , the distance to the Galactic Center. A flat rotation
curve with V0 = 210 km/s is a reasonable compromise between faster rotation for larger
R0 (Levine et al. 2006; McClure-Griffiths & Dickey 2007) and slower rotation for small R0
(Olling & Merrifield 1998). Inside the solar circle we need to allow for non-circular rotation
and therefore the gas velocities are given by the flow model described in subsection 2.2. A
linear transition is used to match the gas flow model for the inner and outer Galaxy between
7 kpc and 9 kpc in Galactocentric radius. The flow model of Bissantz et al. (2003) also has
a few small data holes that are patched by linear interpolation.
While the bar model provides kinematic resolution toward the Galactic Center, we still
face a lack of resolution in the direction of the anticenter, because purely circular rotation
is assumed to apply for r > R0 . Therefore the rotation curve is used only for |b| ≤ 5◦ and
|l| ≤ 165◦. Towards the anticenter, where the kinematic resolution vanishes, we interpolate
the distribution of gas between those derived in 10-degree windows centered on l = 160◦ and
l = 200◦ and use that as a probability function according to which the actually measured
line signal is distributed. At high latitudes (|b| ≥ 5◦ ) the signal is distributed according to
the distance distribution derived for |b| ≤ 5◦ as a prior, weighted by a Gaussian of the height
above the mid-plane, z, for the distance and latitude in question.
The final data cube of deconvolved molecular gas will give the gas density in bins of
100 pc length for the line-of-sight distance, assuming a nominal X-factor X = 2.3 · 1020 mol./cm2 /K/(km s−1
–9–
The actual deconvolution uses distance bins of 50 pc length, though, and follows an iterative
procedure. The internal velocity dispersion of individual gas clouds is determined from the
profiles of narrow lines as
σCO = 3 km/s
(10)
This single-cloud velocity dispersion is small, but still well in the range of those derived in
other studies (e.g. Malhotra 1994). In the Galactic-Center region the velocity dispersion is
expected to be higher than that (Dahmen et al. 1998). Within the central kiloparsec we
therefore use
σCO (r ≤ 1 kpc) = 5 km/s
(11)
The actual deconvolution consists of many steps, each of which is supposed to involve an
individual gas cloud or part thereof. For that purpose the CO line spectrum is convolved with
a Gaussian with half the velocity dispersion of individual gas clouds. The value and velocity
of the peak in the convolved spectrum is determined, which is less influenced by noise than
if determined through the raw spectrum. Tests have shown that the deconvolution tends
to break the total line signal into a few blobs on the line-of-sight, if we place the full peak
line signal at the distance corresponding to its velocity, so an iterative process is required.
Providing both good computational speed and accuracy, a Gaussian with 20% of that peak
value (or the remaining velocity-integrated intensity, whichever is smaller) and a dispersion
as given by Eqs. 10 or 11, i.e.
δWCO
(v − v0 )2
I(v) = √
exp −
,
(12)
2
2 σCO
2π σCO
is subtracted from the original spectrum and the corresponding δWCO value is added to
the vector that represents the density distribution along the line-of-sight, thus ensuring
that negative fluctuations are not propagated to the density distribution. This procedure is
repeated until the velocity-integrated intensity in the remaining CO line spectrum is less than
a specified value, here 1 K km s−1 . The line spectrum that remains when the deconvolution
has terminated should contain only noise. Figure 3 shows for a specific line-of-sight the
original CO line spectrum in comparison with the convolved spectrum, that is used to find
the true peak velocity, and the remaining line spectrum at the end of the deconvolution. To
be noted from the figure is that the remaining spectrum does indeed appear to be essentially
noise. In the present case the remaining integrated line signal is 0.94 K km s−1 . It is possible
that some of that remaining signal is true emission, and more sensitive observations of the
outer Galaxy have in fact found CO line emission at lower level (Nakagawa et al. 2007), but
here we have no information as to the velocity (and hence the distance) that this emission
should be attributed to. This translates to a systematic uncertainty in the reconstructed
column density of molecular gas that can be estimated as
∆NH2 = X ∆WCO ≃ 4 · 1020 atoms cm−2
(13)
– 10 –
for a standard X-factor. Only at high latitude, where the gas column density is low, will this
uncertainty have significance compared with uncertainties in the X-factor, limited coverage,
or measurement uncertainties. In terms of Galactic diffuse γ-ray emission above 100 MeV
the associated uncertainty is 30% of the extragalactic diffuse background as measured with
EGRET (Sreekumar et al. 1998).
In each iteration step we determine the 8 kinematically best-fitting locations using
distance bins of 50 pc length to account for the multitude of possible distance solutions. The
line signal is distributed among these eight solutions with weights that are determined by
three factors: first a Gaussian function in the separation from the midplane,
(z − zc )2
,
(14)
wz = exp −
2 σz2
then a Gaussian function with a HWHM of 8.3 kpc in Galactocentric radius to limit the
placing of gas at large radii on the far side of the Galaxy, which is often kinematically allowed,
but unlikely. The last factors reflects the Jacobian |dv/dD| that arises from transforming
a differential in velocity into a differential in line-of-sight distance, D. In that Jacobian we
have to account for the binning in both velocity and distance. The data cube of the CO line
spectrum provides us with the average intensity per velocity interval δv = 1.3 km/s. The
Jacobian translates this into an associated distance interval ∆v D, over which the line signal
should be distributed,
dv −1
∆v D = (15)
δv .
dD
The distance itself is binned with δD = 50 pc. If ∆v D ≥ δD, which is the standard case,
then the signal must be distributed over neighboring bins, each of which receives a fraction
δD/∆v D of the total signal. Our accounting for 8 possible distance solutions at each iteration
step together with the usually large number of iteration steps ensures that in this case part
of the line signal is indeed attributed to the neighboring distance bins. If ∆v D ≤ δD, then
the signal must nevertheless be distributed over the entire distance bin. In total we can
define weight factors representing the Jacobian as

1
for ∆v D ≤ δD
δv 
wJ =
·
(16)
δD  δD
for ∆v D ≥ δD
∆v D
Gas with forbidden velocity is placed in the distance bins with the best matching velocity,
except toward the inner Galaxy (|l| ≤ 20◦ ) where for a velocity offset of more than 10 km/s
to the nearest allowed velocity we accept only distance bins in the Galactic Center region.
Finally the line-of-sight distribution of gas is reduced to a resolution of 100 pc.
– 11 –
Fig. 3.— The CO1→0 line spectrum in the direction l = 340◦ and b = 0◦ at different stages
of the deconvolution. The top panel gives the original spectrum as reported by Dame et al.
(2001). The middle panel shows that spectrum after convolution with a Gaussian, which
we use find the intensity and velocity of the peak emission, assuming true emission lines are
significantly broader than the velocity bins of the CO spectrum. The bottom panel displays
the remaining spectrum after termination of the deconvolution, which ideally should contain
only noise. The residual spectrum shown in the bottom panel is typical. If the velocity
dispersion (Eq. 10) were chosen too large, negative spikes could appear that arise from
over-subtraction of line wings.
– 12 –
In Eq. 14 we must account for an increase in the thickness of the gas disk with Galactocentric radius. While the variations of σz appear small within the solar circle (Malhotra
1994; Nakanishi & Sofue 2006), a substantial flaring of the molecular gas disk is observed in
the outer Galaxy (Wouterloot et al. 1990; Binney & Merrifield 1998). An analytical approximation to the various results reported in the literature is given by
2
r
r
+ 60
pc
(17)
σz = 60 − 50
R0
R0
Warping of the molecular disk appears insignificant within the solar circle (Malhotra 1994;
Nakanishi & Sofue 2006), and therefore we neglect it altogether. In the outer regions of the
Galaxy the warp in the molecular disk is assumed identical to that of the HI disk and is
given in good approximation by (Binney & Merrifield 1998)
zc = (1, 000 pc) x sin φ + (300 pc) x2 (1 − cos(2 φ))
(18)
where
r − (11 kpc)
and r ≥ 11 kpc
6 kpc
Finally, to somewhat alleviate the near-far ambiguity toward the inner Galaxy, we first
deconvolve the spectra for Galactic latitudes |b| ≥ 1◦ . We then average the deduced gas
density in the near region over 0.9375◦ < |b| < 1.5625◦ and interpolate the result for latitudes
|b| < 1◦ , where they are used as an estimate for the minimum gas density in the near region.
This procedure avoids the placing of the signal from nearby gas clouds to large distances,
where they would correspond to a substantial surface mass density.
x=
3.
Test on simulated data
To test the deconvolution procedure and estimate the nature and strength of deconvolution artefacts, we have simulated a CO line data set using an artificialmodel gas distribution
that consists of a bar and two spiral arms as shown in the top panel of figure 4. One should
note that the simulated line data set is based on the same gas flow model and intrinsic line
widths that are used during the deconvolution, so this test will not show artefacts that arise
from imperfections of the flow model. Its main purpose is to identify the noise level and
those characteristics in the final deconvolved gas distribution that are likely not real, as for
example caused by distance ambiguities or velocity-crowding, i.e. small |V /dD|, where the
inversion of the distance-velocity relation is uncertain. The bottom panel of figure 4 shows
the reconstructed surface mass density. To be noted from the figure are three major types
of artefacts that we will see again in the deconvolutions of the real data set. In the regions
– 13 –
Fig. 4.— (Top panel) The surface mass density in M⊙ /pc2 for the simulated gas distribution,
for which we have calculated hypothetical gas line data. The dashed white lines illustrate the
location of the Galactic bar and two possible logarithmic spiral arms, that would correspond
to the Sagittarius arm and the Norma/Perseus +l arm. White areas have a surface mass
density below the lower limit of the colorbar. (Bottom panel) The reconstructed surface
mass density reproduces the bar and the spiral arms with three major types of artefacts,
labeled with the letters X, O, and W.
– 14 –
indicated by the letter O, in the anticenter and outside the solar circle on the far side of the
Galaxy, the kinematic resolution is poor or nonexistent, and the deconvolution tends to break
up the arms into three quasi-parallel structures. The region labelled W at large negative x
has no kinematic resolution, but receives some signal at zero velocity, which appears here
as a tail on the far side of the Galaxy. The signal in the regions marked with the letter X
corresponds to the far distance solution of gas in the spiral arm that passes the sun at about
1 kpc distance. A detailed inspection shows that the very high reconstructed surface mass
density in the region at (x, y) = (−8., 5.) arises from an unusually wide z-distribution. Signal
in the wing of the line profile of the highest possible velocity near the sun has a velocity, for
which only a far solution exists. The deconvolution code cannot perfectly separate shift on
account of the intrinsic line width from shift arising from the Galactic gas flow, so a fraction
of the signal is attributed to the far solution, which is about 20 times as distant as the near
solution, and so the misplaced signal corresponds to a substantial surface mass density, even
though it is inconspicuous in the distribution in distance of the gas density.
4.
4.1.
Results
The standard gas-flow model
Figure 5 shows the deconvolved gas distribution (more precisely the integrated line
intensity, WCO , per distance bin of 100 pc), for two lines-of-sight, based on the standard gasflow model with bar inclination angle φ = 20◦ . The top panel refers to the direction of the
Galactic Center and can therefore be directly compared with Figures 1 and 2, which show the
velocity-distance relation and the CO line spectrum for that line-of-sight. Even though in
the WCO distribution we see a strong narrow peak near the Galactic Center at 8 kpc distance,
a similar fraction of the line signal is in fact placed between about 9 and 10 kpc distance.
This corresponds to intensity at 50–100 km/s velocity, for which two distance solutions exist
with significantly different |dv/dD|. The two solutions are equivalent in terms of the other
weight factors, so they receive the same intensity in total, which in the case of the larger
distance is spread out over about ten distance bins.
Figure 6 shows the reconstructed surface mass density of molecular gas for the standard
gas-flow model and a constant conversion factor X = 2.3 · 1020 molecules/cm3 /(K km s−1 )
smoothed to about 200 pc resolution. The location of the sun is x = 8 kpc and y = 0.
The artefact labelled W in figure 4 is prominent here as well: The patches of relatively
high surface mass density at large Galactocentric radii on the far side of the Galaxy (at
x . −10 kpc) originate from line signal near zero velocity, for which those large distances
are a valid kinematic solution. In some cases the line intensity at small velocities is so high,
– 15 –
Fig. 5.— The deconvolved integrated CO line intensity per distance bin of 100 pc for the
Galactic Center direction (top panel) and at 20 degrees positive longitude (bottom). Note
the difference in scale.
– 16 –
Fig. 6.— The surface mass density of the Galaxy in M⊙ /pc2 assuming a constant conversion
factor X = 2.3·1020 molecules/cm3 /(K km s−1 ). The dotted white circle outlines the location
of artefacts arising from forbidden velocities. The dashed white lines illustrate the location
of the Galactic bar and two possible logarithmic spiral arms, that would correspond to the
Sagittarius arm and the Norma/Perseus +l arm. The data are smoothed to about 200 pc
resolution to better show the large-scale structure. White areas have a surface mass density
below the lower limit of the colorbar.
– 17 –
that signal corresponding to a few M⊙ /pc2 survives the filtering with the Gaussian prior
that we use to reduce the weights for these solutions.
Also visible in figure 6 are artefacts arising from gas at forbidden velocities in the inner
Galaxy. Gas at forbidden velocities is placed where the corresponding extremum in the
line-of-sight velocity is found. For circular rotation with constant speed the location of that
extremum would delineate a circle of radius R0 /2 that extends from the sun to the Galactic
Center and is indicated by the dotted white line. One can clearly see patches of high surface
mass density that roughly follow the dotted line. While it should be expected that the gas
resides near the location of the peak in the line-of-sight velocity, the spatial concentration of
the gas is most likely exaggerated. The fact that a substantial fraction of the total CO line
signal is placed near the dotted white line indicates that the gas flow model underestimates
the flow velocities in the inner Galaxy. Note, that this kind of artefact is not seen in test
simulation presented in the previous section.
One clearly sees a mass concentration along the Galactic bar where the surface mass
density is often two orders of magnitude higher than at similar Galactocentric radii on the
sides of the bar. Two spiral arms seem to emerge at the ends of the bar. The distribution
of molecular gas supports the notion that those two spiral arms have a small pitch angle.
The dashed white line indicates the location of the Galactic bar according to Bissantz et al.
(2003) and, for illustration, two logarithmic spiral arms with pitch angle 11.5◦ , that emanate
from the ends of the bar at R = 3.5 kpc. On the near side this would be the Norma arm
that circles around the Galactic Center and reappears as the Perseus +l arm in the notation
of Vallée (2002). Emerging on the far side and closely passing by the sun would be the
Sagittarius arm. To be noted from the figure is that the distribution of molecular mass is
roughly consistent with those two arms. There is excess molecular material that one may
associate with two other arms, for example the gas near x = 5 kpc and Y = 0 kpc would
mark the Scutum arm. The gas between the sun and the outer Perseus +l arm would lie in
the Perseus arm. While certain structures in the map can be associated with those arms as
discussed in the literature, it is not a priori clear that those structures are real. A comparison
with the deconvolved mass distribution for the simulated data set in Fig. 4 shows that the
excess material coincides with two artefacts marked by an X at (x, y) = (−2, 3) kpc and
at (x, y) = (−2, −7) kpc, that correspond to the far solution of the nearby Norma arm and
Sagittarius arm, respectively. On the other hand, the gas distribution in the SPH simulation
of Bissantz et al. (2003) does not simply follow the logarithmic spiral arms, in particular not
within the inner few kpc. While the signal at (x, y) = (−2, −7) kpc is close to the boundary of
the SPH simulation region, thus hindering a fair assessment of their relevance, the structure
near (x, y) = (−2, 3) kpc has a clear counterpart in the gas distribution according to the gas
model of Bissantz et al. (2003).
– 18 –
Fig. 7.— The surface mass distribution in the inner 10 kpc × 10 kpc of the Galaxy in
full resolution. As before the units are M⊙ /pc2 assuming a constant conversion factor X =
2.3 · 1020 molecules/cm3 /(K km s−1 ). White areas have a surface mass density below the
lower limit of the colorbar.
– 19 –
Fig. 8.— Blow-up of the inner 2 kpc × 2 kpc of Figure 7. The diamond marks the position
of the Galactic Center. The solid circle outline the massive cold torus structured inferred by
Launhardt et al. (2002). The dotted lines indicate the central molecular zone according to
the model of Ferrière et al. (2007). The inner ellipse corresponds to the peak in surface mass
density, and the outer ellipse outline the perimeter where the density has fallen to 1/e of the
peak value. White areas have a surface mass density below the lower limit of the colorbar.
– 20 –
Figure 7 shows the surface-mass distribution within 5 kpc from the Galactic Center with
standard resolution of 100 pc. As before the dashed lines indicate the bar and two logarithmic
spiral arms, whereas the dotted lines outlines the circle on which gas at forbidden velocity
may be projected. Many of the structures shown in Figs. 6 and 7 do not appear as clean
and narrow as those in the SPH simulations of Bissantz et al. (2003), but the fact that the
most salient features can be recovered lends credibility to their existence in the Galaxy.
Particularly interesting are the pseudo-arms that emerge from the bar at about 2 kpc from
the Galactic Center. Our deconvolution shows similar structures at (x, y) = (2, 0) kpc and
(x, y) = (2, 0) kpc, although a significant fraction of the latter is clearly gas at the Galactic
Center that is misplaced at the far solution (compare Fig. 1).
Within 1 kpc from the Galactic Center the model velocities are affected by the limited
resolution of the SPH simulation. One may therefore not expect the gas distribution to be
well reproduced. Figure 8 shows the reconstructed distribution of molecular gas within 1 kpc
of the Galactic Center. To be noted from the figure is the concentration of molecular gas in
three segments that may be interpreted as fragments of an elongated ring that is somewhat
off-center, shifted toward positive longitudes (negative y). The overall geometry resembles
the expanding molecular ring proposed much earlier by Scoville (1972), but stretched along
the line-of-sight. Fig. 8 should be interpreted very carefully, because the limited resolution
of the gas flow model has a significant impact on the reconstructed gas distribution. In fact
we find that it depends on how one interpolates the gas velocity between the grid points
at which the average flow velocity is computed in the SPH simulation. For comparison we
indicate the location of the massive cold torus found by Launhardt et al. (2002) using IRAS
and COBE/CIRBE data by the solid white line. We can further compare our results with
those of Sawada et al. (2004) who used only observational data (emission vs. absorption)
and no kinematic tracing. They find an center-filled ellipsoidal configuration with large
inclination angle to the line-of-sight. The peak in surface density appears at x ≈ −0.03 kpc
and y ≈ −0.15 kpc (our coordinate system) and may be identified with Sgr B and what
they denote the 1.3◦ region. In contrast, we find the peak in mass density clearly behind
the Galactic Center at x ≈ −0.3 kpc, and the gas distribution is closer to a ring or two
arms as suggested by Sofue (1995). Ferrière et al. (2007) have proposed a model of the
central molecular zone that appears to be a compromise between the various configurations
discussed in the literature. The overall appearance of the central molecular zone is that of an
ellipse with a slight reduction of the density toward the center, which is indicated in figure 8
by dotted lines. The inner ellipse corresponds to the peak in surface mass density, and the
outer ellipse outline the perimeter where the density has fallen to 1/e of the peak value. The
major axis of the ellipse is nearly perpendicular to the line-of-sight, whereas in our model it
is significantly stretched along the line-of-sight, probably as a result of the limited resolution
– 21 –
of the gas flow model. We find no counterpart to the kpc-scale Galactic Bulge disk in the
model of Ferrière et al. (2007), in fact our reconstructed surface mass densities to the sides
of the bar are very much lower than in her model, if one accounts for a small X-factor in
the Galactic Center region. Both in the SPH simulation of Bissantz et al. (2003) and in our
surface density maps one sees a concentration of gas along the bar and large voids to the
side, which are intersected by pseudo-arms.
4.2.
Alternative gas-flow models
The gas-flow models are not perfect, for example they may not match both the observed
terminal-velocity curve (TVC) in the inner Galaxy and the orbit velocity at the solar radius
to better than 5%. To investigate the impact of the particular choice of the gas-flow model
on the reconstructed gas distribution, we here show deconvolutions based on two alternative
models. The first is also derived from a SPH simulation of Bissantz et al. (2003), but in this
case the bar is assumed to be inclined at φ = 30◦ . This model should reproduce the terminal
velocity curve in the longitude range 10◦ ≤ l ≤ 60◦ , and thus be qualitatively similar to the
standard model, except the bar parameters are different and the overall fit of the model to
the lv-diagram is slightly worse but still in agreement with observations. Figure 9 shows the
reconstructed surface mass density for this alternative gas-flow model. To be noted from the
figure are the large voids at Galactocentric radii R = (7 − 8) kpc, whereas the mass density
in the inner 6 kpc is more homogeneous than for the standard model. Figure 9 clearly shows
an increased amount of material in artefacts along the dotted circle, which indicates that
the standard model is more in agreement with the observed gas flow, as expected.
Whereas the first alternative gas-flow model should still be a fair approximation of the
actual velocity distribution in the inner Galaxy, we now also use a model that is intentionally
distorted to no longer reproduce the TVC in the inner Galaxy. For that purpose we rotate
the standard gas-flow model by another 20◦ , so that the bar inclination is φ = 40◦. As
shown in Fig. 10, the resultant gas distribution is significantly changed. There is a large
void between the sun and the Galactic Center at about (x, y) = (5, −1) kpc, where the lineof-sight velocity in the flow model no longer matches any signal in the CO line. A second
large void appear in the lower left of the plot, corresponding to a Galactic longitude l ≈ 30◦
and distances around 15 kpc. A relatively high surface mass density is found on the far side
of the Galaxy at 7 kpc Galactocentric radius which is most likely misplaced line signal from
the Galactic Center region.
– 22 –
Fig. 9.— The surface mass density in M⊙ /pc2 for the alternative gas-flow model with bar
inclination φ = 30◦ . The dashed line indicating the location of the bar and two logarithmic
spiral arms is plotted accordingly. White areas have a surface mass density below the lower
limit of the colorbar.
– 23 –
Fig. 10.— The surface mass density in M⊙ /pc2 for the standard gas-flow model rotated
by another 20◦ , so that the bar inclination is φ = 40◦ . This gas-flow that is intentionally
distorted to no longer reproduce the actual velocity distribution in the inner Galaxy.
– 24 –
5.
Summary
We have derived a new model of the distribution of molecular gas in the Galaxy based on
CO line emission (Dame et al. 2001). For that purpose we use a gas-flow model derived from
smoothed particle hydrodynamics (SPH) simulations in gravitational potentials based on the
NIR luminosity distribution of the bulge and disk (Bissantz et al. 2003). Besides providing
a more accurate picture of cloud orbits in the inner Galaxy, a fundamental advantage of this
model is that it provides kinematic resolution toward the Galactic Center, in contrast to
standard deconvolution techniques based on purely circular rotation.
To test the deconvolution procedure and estimate the nature and strength of deconvolution artefacts, we have applied it to a simulated CO line data set based on a model
gas distribution that consists of a bar and two spiral arms. We have also deconvolved the
actual observed CO data using alternative gas-flow models, one of which is intentionally
distorted to no longer reproduce the actual velocity distribution in the inner Galaxy. The
reconstructed distribution of surface mass density is significantly affected in the case of the
ill-fitting gas-flow model. When using gas-flow models that reproduce the terminal-velocity
curve, but are based on different bar inclination angles, the reconstructed gas distribution
are much more alike. In particular, the deconvolution is robust against a simple rescaling
of the gas-flow velocities by a few percent. A comparison of the surface mass density determined using feasible and unfeasible gas flow models shows that in the latter case the
resulting surface mass density is also unfeasible. Examples of that are the very low surface
mass density regions around (x, y) = (5, −1) kpc and (x, y) = (−8, −8) kpc, and the strong
feature at (x, y) = (−7, −1) kpc in Figure 10. Hence, the comparison of the surface mass
densities from the various gas flow models strongly indicates that the result of the deconvolution algorithm is robust against moderate variations in the underlying gas flow model.
On the other hand, it is sensitive enough to changes in the gas flow model to discriminate
the surface mass density solutions based on feasible gas-flow models against those based on
unfeasible flow models.
We now describe our model for the surface mass density of the gas in more detail. In the
model we find a concentration of mass along the Galactic bar where the surface mass density
is often two orders of magnitude higher than at similar Galactocentric radii of the sides of the
bar. Two spiral arms seem to emerge at the ends of the bar, which have a small pitch angle
∼ 12◦ . While certain structures in the surface density distribution may be associated with
two more spiral arms as discussed in the literature (Vallée 2002), the evidence for those arms
provided by this deconvolution is not strong, and localizing spiral arms based on kinematics
and CO line data alone is difficult. We also reproduce a concentration of molecular gas in
the shape of an elongated ring around the Galactic Center that resembles the massive cold
– 25 –
torus found by Launhardt et al. (2002), but is broken up and somewhat stretched along the
line-of-sight, probably as a result of the limited resolution of the gas flow model.
Models of the three-dimensional distribution of molecular gas in the Milky Way Galaxy
can be used in many applications, for example to analyze the diffuse Galactic gamma-ray
emission that will be observed with GLAST. Knowledge of the gas distribution is essential
for studies of the cosmic-ray gradient in the Galaxy, but also for investigation of small-scale
variations in the density and flux of cosmic rays. Our gas model will be publicly available
at http://cherenkov.physics.iastate.edu/gas.
Support by NASA grant NAG5-13559 is gratefully acknowledged.
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This preprint was prepared with the AAS LATEX macros v5.2.